论文标题
一种用于使用Markov融合的贝叶斯模型的数值稳定算法
A numerically stable algorithm for integrating Bayesian models using Markov melding
论文作者
论文摘要
当统计分析考虑多个数据源时，马尔可夫融合提供了一种结合特定于源贝叶斯模型的方法。马尔可夫融合在一起，将具有共同数量的子模型融合在一起。一个挑战是，该数量的先前可以是隐式的，并且必须估算其先前的密度。我们显示，在此密度估计中，误差使马尔可夫融合了不稳定和不可靠的两阶段马尔可夫链蒙特卡洛采样器。我们提出了一种强大的两阶段算法，该算法使用加权样品估算所需的先前边际自密度比，从而显着提高了分布尾部的精度。该算法的稳定版本是务实的，并提供了可靠的推断。我们使用证据综合来推断HIV患病率以及A/H1N1流感的证据综合证明了我们的方法。
When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the prior for this quantity can be implicit, and its prior density must be estimated. We show that error in this density estimate makes the two-stage Markov chain Monte Carlo sampler employed by Markov melding unstable and unreliable. We propose a robust two-stage algorithm that estimates the required prior marginal self-density ratios using weighted samples, dramatically improving accuracy in the tails of the distribution. The stabilised version of the algorithm is pragmatic and provides reliable inference. We demonstrate our approach using an evidence synthesis for inferring HIV prevalence, and an evidence synthesis of A/H1N1 influenza.
